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Managing Portfolios: Theory Chapter 3

Managing Portfolios: Theory Chapter 3. Modern Portfolio Theory Capital Asset Pricing Model Arbitrage Pricing Theory. Learning Objectives. Basics of Investment Theories Review Efficient Markets Hypothesis (EMH) Modern Portfolio Theory (MPT) Application and Implications

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Managing Portfolios: Theory Chapter 3

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  1. Managing Portfolios: TheoryChapter 3 Modern Portfolio Theory Capital Asset Pricing Model Arbitrage Pricing Theory All Rights Reserved

  2. Learning Objectives • Basics of Investment Theories • Review Efficient Markets Hypothesis (EMH) • Modern Portfolio Theory (MPT) • Application and Implications • Capital Asset Pricing Theory (CAPM) • Application and Implications • Arbitrage Pricing Theory • The “UFO” of Investment Theory All Rights Reserved

  3. Basics of Investment Theories • Investment Returns are a function of Risk • Risk is a function of Uncertainty • The degree of uncertainty may be defined by a probability distribution • The shape of [future] probability distributions are much more art than science • Bottom line: don’t be fooled or led astray by the mathematical elegance of the theories to be discussed. All Rights Reserved

  4. Efficient Markets Theory • Efficient Markets Hypothesis (EMH) • Implication: you cannot consistently beat the market • Prices Reflect all information • Past (Weak form efficiency) • Present or New (Semi-Strong form efficiency) • Inside (Strong form efficiency) • Results of Academic Research • Markets mostly weak form efficient • Several Anomalies question semi-strong efficiency • Insiders consistently outperform the market • Best you can do is manage risk • More on EMT/EMH in Chapter 5 All Rights Reserved

  5. Modern Portfolio Theory (Markowitz) • MPT: 2 Sources of Risk • Variation • Covariance • Risk Management Strategy • Hold a diversified portfolio of assets • The more assets, the lower the risk • Assets are considered in terms of the variance and covariance they add to the portfolio All Rights Reserved

  6. Modern Portfolio Theory (Markowitz) • Riskiness of a Two-Asset Portfolio • sP2 = w12 s12 + w22 s22 + 2 w1 w2 cov1,2 • Subject to: w1 + w2 = 1 • Covariance (Correlation [r]) • 2 assets may covary • Positively (move in same direction) r > 0 • Not at all (zero – no correlation) r = 0 • Negatively (move in opposite directions) r < 0 • Least risk 2-asset portfolio? When cov1,2 < 0 • Most risky 2-asset portfolio? When cov1,2 > 0 All Rights Reserved

  7. Modern Portfolio Theory (Markowitz) • Correlation (2 assets) • Positive • Negative • Zero (random) • Non-Linear • Linear All Rights Reserved

  8. Modern Portfolio Theory (Markowitz) • Return on a Two-Asset Portfolio • E (Rp) = w1 E(R1) + w2 E(R2) • General Form of MPT • E(RP) = S wi E (Ri) • sP2 = S wi2si2 + SS wi wj covi,j • Subject to: S wi = 1 All Rights Reserved

  9. Efficient Frontier • Locus of all efficient portfolios • The shape of the EF is a function of the average correlation of assets in the portfolio • Portfolios are mean [return] – variance efficient when they place on the EF (see point MVP). All Rights Reserved

  10. Selecting a Portfolio • Risk Preferences or Indifference • Investors are generally assumed to be risk averse. • Prefer less risk to more for a given rate of return • Prefer a higher return for a given level of risk • Indifference curves tell us something about our utility functions relative to wealth. • How much do we value an additional unit of wealth? • How much are we willing to risk to obtain it? • See Figure 3-8 on page 3.20 All Rights Reserved

  11. Indifference Curves (Examples) All Rights Reserved

  12. Tobin MPT Extension • Major drawbacks to MPT • Computing Variance-Covariance Matrix • Mathematics for Selecting Assets • James Tobin (1958): suppose we consider a risk-free (RF) asset combined with the EF • A straight line EF results • 2-Asset PF: RF and M (risky [market] portfolio) • See Figure 3-14 on page 3.31 • Lend and Borrow at the RF rate All Rights Reserved

  13. Tobin: Add the Risk-free Asset All Rights Reserved

  14. Market Portfolio as Construct • Hypothetical portfolio representing each investment asset in the world in proportion to its relative weight in the universe of investment assets • Index Construction • Value weighted • Equal weighted All Rights Reserved

  15. Separation Theorem • Return to any efficient portfolio and its risk can be completely described by appropriate weighted average of two assets • the risk-free asset • the market portfolio • Two separate decisions • What risky investments to include in the market portfolio • How one should divide one’s money between the market portfolio and risk-free asset All Rights Reserved

  16. Capital Asset Pricing Theory (Sharpe) • The concept of Beta (b) • Assuming the existence of a mean and variance efficient market portfolio, how can we construct an portfolio of risky assets with a known risk attribute? • More or less risky than M • Beta = a measure of asset risk relative to the market portfolio (M). • b = covi,M / sM2 • b = (ri,Msi) / sM All Rights Reserved

  17. Capital Asset Pricing Theory (Sharpe) • Implications of Beta Value • Beta < 0: moves opposite to the market • Beta = 0: independent of the market • 0 < Beta < 1: less risky than market • Beta = 1: risk identical to the market • Beta > 1 => more risky than market All Rights Reserved

  18. Capital Asset Pricing Theory (Sharpe) • Estimating Beta (CAPM) • b is a simple OLS regression coefficient • General Form: y = a + bx + e • OLS: Ri = a + b RM • CAPM: E (Ri) = E (RF) + b {E (RM) – E (RF)} • {E (RM) – E (RF)} is defined as the risk premium • B is defined as the amount of risk • b {E (RM) – E (RF)} is the price of risk • ri = rf + (rm – rf) bi • Portfolio Beta = S Wibi All Rights Reserved

  19. Capital Asset Pricing Theory (Sharpe) • The Capital Market Line (CML) • Graphing CAPM for market portfolio • The Security Market Line (SML) • Graphing CAPM for security i ri = rf + (rm – rf) bi All Rights Reserved

  20. Capital Asset Pricing Theory (Sharpe) • Market Risk vs. Nonmarket Risk i2 = (beta2 x M2 ) + eta2 Total risk = market risk + nonmarket risk All Rights Reserved

  21. CAPM Issues • What return frequency should we use? • Daily, weekly, monthly, quarterly • What constitutes the market portfolio? • SP500 as a proxy • Other proxies yield different b estimates • Central tendency characteristic of Beta • Coefficient of Determination (R2) varies widely for individual securities. All Rights Reserved

  22. Arbitrage Pricing Theory (APT) • Generalized Multi-Factor Pricing Model • Factors are the Eigen values derived from a variance covariance matrix. • Factors are said to “load” on economic/market constructs. • Biggest problem is the nature and reliability of loading. All Rights Reserved

  23. Woerheide's Final Thoughts on Portfolio (Investment) Theories • Uniform Principal and Income Act (1931) • Prudent man rule has evolved to prudent investor • A [poor?] model is better than no model • Departure point for how we think about what is happening in security markets All Rights Reserved

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